Posted by: Bryan Goh in: Uncategorized
Let’s do a little experiment. Lets take 1000 fair coins. Let’s give them names and flip them to see which ones come up heads and which ones come up tails. Now let’s take another 1000 fair coins and do the same, given them unique names and flip them recording which ones come up heads and which ones tails. While we are flipping this second batch, flip also the first batch and record their results. Now add another 1000 coins naming them, flipping them and recording their results. Do this for the previous batches as well. Continue doing this until you have 8 batches of 1000 coins.
Using simple rules of probability, of all the coins that have been flipped 8 times, that is from the first batch of course, how many would one expect to have come up heads precisely 8 times? Being fair coins, the number would be 0.5 raised to the 8th power X 1000, or roughly 4 coins. Of all the coins that have been flipped precisely 7 times, that is from the second batch, one would expect the number of coins to have only ever come up heads in every toss to be 0.5 raised to the 7th power X 1000, or roughly 15.
8 heads out of 8 tosses: 4 coins in 1000
7 heads out of 7 tosses: 8 coins in 1000
6 heads out of 6 tosses: 15 coins in 1000
5 heads out of 5 tosses: 30 coins in 1000
Thus, out of 8000 coins there are 57 coins who have never come up tails. Now supposing we loosely defined heads as the ability to generate good returns in a given year and tails the complement, and if we gave the coins strange names like ABC Capital, DEF Capital, GHI Partners, JKL Asset Management and so on…
Here in our database of 8000 coins there are 57 who have never had an unsuccessful year. Because we stopped our count at 5, you could compare this to searching a hedge fund database for funds with at least years of track record and have been successful in every year of their operating history.
The thing about the coins though is that the probability that one chosen from that 57, would have no more than an even chance of coming up heads next flip.
The above example is just an illustration. The definition of successful in a given year has not been clearly made. What is a successful year for a hedge fund? It depends on the level of risk they take. It depends on conditions in the markets. Depending on how demanding you are, success could be a very tough condition and the probability of being successful could be significantly less than 50%.
Let’s do some calibration. Let us say that 5% of all managers have a good 3 year track record. We are thus defining success. This implies that success occurs with 37% probability. Using this probability we go through our calculation again and find that there are
0 managers with 8 years of unblemished track record.
1 with 7 years
2 with 6 years
7 with 5 years
18 with 4 years
Thus 28 with at least 4 years of unblemished track record. That’s still quite a lot. And on the information we have, any one of these 28, thus chosen would have a 37% chance of being successful in the next year.